Hysteresis loops and multi-stability: From periodic orbits to chaotic dynamics (and back) in diatomic granular crystals

• Published in: Europhysics letters Vol. 101; no. 4; p. P1
• Main Authors: Hoogeboom, C, Man, Y, Boechler, N, Theocharis, G, Kevrekidis, P G, Kevrekidis, I G, Daraio, C
• Format: Journal Article
• Language: English
• Published: Les Ulis IOP Publishing 01-02-2013
• Subjects: Chaos theory; Crystals; Dynamical systems; Dynamics; Hysteresis; Mathematical models; Nonlinear dynamics; Nonlinearity
• ISSN: 0295-5075; 1286-4854

This paper considers a statically compressed diatomic granular crystal, consisting of alternating aluminum and steel spheres. The combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. Through both numerical simulations and experiments, the paper finds that the interplay of nonlinear surface modes with modes caused by the driver create the possibility, as the driving amplitude is increased, of limit cycle saddle-node bifurcations beyond which the dynamics of the system becomes chaotic. In this chaotic state, part of the applied energy can propagate through the chain. The paper also finds that the chaotic branch depends weakly on the driving frequency, and speculates a connection between the chaotic dynamics with the gap openings between the spheres. Finally, the paper observes hysteretic dynamics and an interval of multi-stability involving stable periodic solutions and chaotic ones.